Decomposition algorithms decompose an A matrix has a product of several specific
matrices from which they can solve A × X = B in least squares sense: they find X
such that ||A × X - B|| is minimal.

Some solvers like FieldLUDecomposition can only find the solution for
square matrices and when the solution is an exact linear solution, i.e. when
||A × X - B|| is exactly 0. Other solvers can also find solutions
with non-square matrix A and with non-null minimal norm. If an exact linear
solution exists it is also the minimal norm solution.